Abstract : One of the more frequently quoted papers in fluid dynamics is the article by Karl Pohlhausen, 'Zur naherungsweisen Integration der Differentialgleichungen der laminaren Grenzschicht,' which appeared on pages 252-268 of Volume I of the Zeitschrift fur angewandte Mathematik und Mechanik. Consequently, it seems appropriate to make an English translation of the original German paper widely available. While the approximate integration technique which the article outlines has been superseded in large measure by substantial improvements, the kernel of all useful methods is given in the original paper. Moreover, many other important results of permanent value to fluid dynamics are presented, e.g., a mathematical derivation of Karman's momentum equation from the boundary layer equation and the mathematical description in finite closed form of the steady two dimensional laminar flow in a converging channel according to boundary layer theory.